10/11/2020 | We will start the year with a wide variety of competition style problems. [Show less] |

10/18/2020 | We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares. [Show less] |

10/25/2020 | We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares. [Show less] |

11/1/2020 | We will study the limitations of polynomials as prime generating functions. [Show less] |

11/8/2020 | We will study recursive formulas for generating primes. [Show less] |

11/15/2020 | We introduce some classic algorithms and the notion of runtime. [Show less] |

11/22/2020 | Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem. [Show less] |

12/6/2020 | We prove the Fundamental Theorem of Algebra with a focus on graphing. [Show less] |

12/13/2020 | The students battle it out in a full class Kahoot competition. [Show less] |

1/10/2021 | [Show less] |

1/17/2021 | We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem. [Show less] |

1/24/2021 | We will explore many interesting results about graph coloring. [Show less] |

1/31/2021 | We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory. [Show less] |

2/7/2021 | Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions. [Show less] |

2/21/2021 | We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric. [Show less] |

2/28/2021 | We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces. [Show less] |

3/7/2021 | In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index. [Show less] |

3/14/2021 | [Show less] |

4/4/2021 | Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits. [Show less] |

4/11/2021 | Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits. [Show less] |

4/18/2021 | We will show that certain regions of Euclidean space must contain integer lattice points. [Show less] |

4/25/2021 | We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes. [Show less] |

5/2/2021 | We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes. [Show less] |

5/9/2021 | [Show less] |

5/16/2021 | We will define what it means for a sequence to converge in different metric spaces. We will explore many different examples like convergence with the taxicab metric or the discrete metric. [Show less] |

5/23/2021 | We define the notion of a continuous function using limits in arbitrary metric spaces. We apply the Intermediate Value Theorem to a range of functions on the real line. [Show less] |

6/6/2021 | [Show less] |